The subject invention relates to encryption of information using public key encryption technology. (By xe2x80x9cpublic keyxe2x80x9d encryption herein is meant encryption technology which uses pairs of keys: a public key, which is published or made publicly known; and a corresponding private key, kept secret by a user.) More particularly it relates to the certification of public keys by a plurality of certifying authorities.
Using public key encryption anyone can encrypt a message with a public key and have assurance that only a user (i.e. a party having the corresponding private key) can decrypt it, and a user can xe2x80x9csignxe2x80x9d a message using the corresponding private key and anyone can use the public key to ascertain if the message originated with the user. (A message is xe2x80x9csignedxe2x80x9d by deriving encrypted information in a known manner from the message.)
Because public keys can be distributed so widely, it will in general be the case that persons communicating with users of public key systems will not be in direct contact with the users and will not be able to directly determine the identity and/or characteristics of the putative users of a public key system. For example a vendor who receives a purchase order signed by the user of a public key which is purportedly that of an authorized agent of the buyer may need to know, but have no way of directly determining, the actual authority of the user. Similarly proof of payment systems, in particular postage meters, which generate indicia encrypted using public key systems as proof of payment have recently been developed by the assignee of the present application and others; and, given the hundreds of thousands of postage meters in service, it is clear that the postal services will face a severe problem in assuring that indicia purportedly generated by a meter corresponding to a particular public key is in fact generated by an authorized postage meter.
To overcome the difficulties inherent in authenticating public keys numerous schemes for issuing certificates for public keys have been proposed. In such schemes, a trusted third party (hereinafter sometimes a xe2x80x9ccertifying authorityxe2x80x9d) provides parties who wish to communicate with a user with a certificate containing the user""s public key, the certificate serving to evidence the third party""s assurances as to the identity or characteristics of the user. In the simplest case such certificates are no more than entries in a directory delivered through a secure channel. More generally the certifying authority will use an encryption technology to deliver the certificate.
In U.S. Pat. No. 4,853,961; for: xe2x80x9cReliable Document Authentication Systemxe2x80x9d; to: Pastor, a public key for a postage meter is encrypted with a third party""s private key and included in the meter indicia. The postal service uses the third party""s public key to recover the meter public key and decrypt the encrypted message which serves to validate the indicia.
In U.S. Pat. No. 5,661,803; for: xe2x80x9cMethod of Token Verification in a Key Management Systemxe2x80x9d; to: Cordery et al., a method of token verification in a key management system is disclosed.
In U.S. Pat. No. 5,680,456; for: xe2x80x9cMethod of Manufacturing Generic Meters in a Key Management Systemxe2x80x9d; to: Baker et al., a method for manufacturing transaction evidencing devices such as postage meters includes the steps of generating a master key in a logical security domain of a key management system and installing the master key in a postage meter.
In U.S. Pat. No. 5,742,682; for: xe2x80x9cMethod of Manufacturing Secure Boxes in a Key Management Systemxe2x80x9d; to: Baker et al., a method of manufacturing a secure box in a key management system is taught.
In U.S. Pat. No. 5,805,701; for: xe2x80x9cEnhanced Encryption Control System for a Mail Processing System Having Data Center Verificationxe2x80x9d; to: Ryan, Jr., a key control system comprising generation of a first set of master keys and assigning the keys to a corresponding plurality of postage meters is taught.
In U.S. application Ser. No. 08/133,416; by: Kim et al.; filed Oct. 8, 1993, a key control system comprising generation of a first set of master keys and assigning the keys to a corresponding plurality of postage meters is taught. Keys may be changed by entry of a second key via encryption with a first key.
In U.S. application Ser. No. 08/772,739; by: Cordery; filed Dec. 23, 1996, a method for controlling keys used in the verification of encoded information generated by a transaction evidencing device and printed on a document is taught.
While the above methods are successful in achieving their intended purpose they are disadvantageous in that they are computationally complex, may produce certificates which are large and inflexible, and may require special hardware.
The following references contain information useful to a general understanding of elliptic curve encryption and certification of public keys.
Secure Hash Standardxe2x80x94FIPS PUB 180-1,xe2x80x9d Apr. 17, 1995.
Digital Signature Standardxe2x80x94FIPS PUB 186,xe2x80x9d May 19, 1994 and Change 1, Dec. 30, 1996.
ANSI X9.62, Elliptic Curve Digital Signature Algorithm Standard (ECDSA), Working Draft, Jan. 15, 1997.
ISO/IEC 9594-8 (1995). Information Technologyxe2x80x94Open Systems Interconnectionxe2x80x94The Directory: Authentication Framework.xe2x80x9d
PKCS #10: Certification Request Syntax Standard, An RSA Laboratories Technical Note,xe2x80x9d Version 1.0, December 1993.
Another method of key certification based upon elliptic curve public key encryption technology has been developed by the Certicom Corporation. (The use of elliptic curve encryption technology is known and a more detailed description of its use, beyond what is given below in the context of certification of public keys, is not required for an understanding of the subject invention.)
Elliptic curve encryption is an example of a cryptographic algorithm based on application of an binary additive operator to points in a finite group. In elliptic curve encryption a finite group of points [P] of order n is defined on an elliptic curve. A binary additive operator [+] (hereinafter sometimes xe2x80x9cpoint additionxe2x80x9d) is defined on the group [P] such that P [+] Pxe2x80x2 is a point in [P]. A more detailed, graphical description of point addition is shown in FIG. 1. As is known to those skilled in the cryptographic art, disjoint curve 10 has the general form y2=x3+ax+b defined over the finite Galois field GF(pm) where p is a prime number other than 2 and m is an integer. Over the Galois field GF(2m) the curve has the form y2+xy=x3+ax+b. It can be shown that groups of discrete points [P] of order n can be defined on curve 10, where n is preferably a number on the order of at least 50 decimal digits in order to provide sufficient security for encrypted information.
As is seen in FIG. 1 curve 10 is symmetric about the x axis so that for any point (x,y) on curve 10 its reflection around the x axis R(x,y)=(x,xe2x88x92y) is also on curve 10.
For two points P,Pxe2x80x2 in [P] it can be show that there exists a unique point R(P [+] Pxe2x80x2) which is a third point common to straight line 12 defined by P and Pxe2x80x2 and curve 10. P [+] Pxe2x80x2 is defined as R(R(P [+] Pxe2x80x2).
FIG. 2 shows the special case for computation of P [+] P. Straight line 14 is defined as tangent to the closed portion of curve 10 and intersecting point P, and R(P [+] P) is defined as the second point common to line 14 and curve 10.
A second operation K*P (herein after sometimes xe2x80x9cpoint multiplicationxe2x80x9d) is defined as the application of [+] to K copies of a point P. FIG. 3 geometrically illustrates computation of 5*P by successive computation of the points P[+]P=2*P, 2*P[+]2*P=4*P, 4*P[+]P=5*P. Point multiplication is the basic operation underlying elliptic curve encryption and has the property that computation of K from knowledge of the group [P], a particular point P, and K*P is hard.
By xe2x80x9chardxe2x80x9d as used herein in regard to computation is meant a computation wherein the time required increases faster than the order of the operands (log n) and preferably exponentially or faster with log n . This means that where K is of order n, the order of [P], and n is chosen large enough the cost, in time or money, of computing K from knowledge of the definition of [P], P, and K*P can be made arbitrarily large while the cost of other computations relating to encryption or decryption remains relatively low and practicable. Of course those skilled in the encryption art will recognize that, even though encryption and decryption can in principle be carried out by manual computation, the possibly of an attack on an encryption scheme using modem computer technology requires that, in practice, the order n be so great that even the relatively easy computations must be carried out by automated encryption stations; e.g. special purpose, or specially programmed general purpose, digital processing systems.
Point multiplication has been described in terms of the group represented by point addition on a discrete elliptic curve. In other embodiments the subject invention can be implemented using any group representation where determining K is hard given the point P and the point formed by combining K copies of point P by repeated application of the group additive point operation. Accordingly, unless otherwise stated the terms xe2x80x9cpoint P and group [P]xe2x80x9d as used herein are intended to include any elements, e.g. integers, functions, permutations, etc, as well as spatial points, for which a binary operation and corresponding group having the necessary properties as described above can be defined.
In elliptic curve encryption a user U has a private Keyu and a corresponding public Keyu*P; where P is a point in [P]. P is published or publicly known. To generate a certified public key in accordance with the above mentioned Certicom encryption scheme user U (i.e. a station operated by user U) generates and keeps secret a random number rU; and computes and sends to a certifying authority CA the point rU*P. Certifying authority CA has a private KeyCA and a public key KeyCA*P Upon receipt of rU*P authority CA generates a random number rCA and computes and publishes a certificate including a point, rU*P [+] rCA*P, wherein rCA is a random number generated by the CA (i.e. by the CA station). Authority CA, which is presumed to have the capability to directly determine the identity or characteristics of user U, also generates information IDU about U includes IDU in the certificate. Certifying Authority CA then returns an integer derived from the CA""s private key and the certificate to the user station which uses that integer to compute key Keyu in such a manner that a party communicating with user U can compute KeyU*P from the certificate and the certifying authority""s public key KeyCA; providing evidence that the certifying authority has linked user U, KeyU*P, and IDU.
The above described certification scheme is believed to be advantageous in that it is computationally simpler, produces smaller certificates, and does not require special secure hardware. However it does not address the situation where a party communicating with a user may need assurance that more than one authority has certified the public key of a user. For example a Post Office which wishes to verify encrypted metered mail may need assurance that the putative public key of a meter has been certified by the meter manufacturer as well as one or more agencies of the USPS Accordingly it is an object of the subject invention to provide a method for controlling, and distributing information among, encryption stations for a user and a plurality of certifying authorities to publish related information such that a party communicating with the user can determine the users public key with assurance that the key has been certified by each of the authorities.
The above object is achieved and the disadvantages of the prior art are overcome in accordance with subject invention which includes a method for controlling, and distributing information among, a plurality of stations, one of said stations being a user station operated by a user U to generate a private encryption key KeyU and others of said stations being certifying stations operated by a plurality of certifying authorities for publishing related information, so that a corresponding public key KeyU*P of said user U can be determined by a party communicating with said user U from said published related information with assurance that said public key KeyU*P has been certified by each of said plurality of certifying authorities CA; programmable apparatus for carrying out the method, and portable data storage media for storing signals representative of program code for controlling the apparatus to carry out the functions said method. In accordance with the method of the subject invention the stations perform the steps of defining a finite group [P] with a binary operation [+] and publishing a point P in said group; and defining and publishing a binary operation K*P, where K is an integer and P is a point in said group, such that K*P is a point in said group computed by applying said operation [+] to K copies of said point P, and computation of K from knowledge of the definition of said group [P], said point P, and K*P is hard. One of the certifying stations is controlled to publish a certificate CERTu for said user U, wherein;
CERTU=(rU+sum(rCAi))*P; and wherein
rU is a random integer known only to said user U and sum(rCAi) is a sum of a plurality of random integers rCAi, an ith one of said certifying stations generating an ith one of said random integers rCAi. Another one of the certifying stations is controlled to publish a message M. The certifying stations also generate a plurality of integers Ii, and send at least the sum of integers Ii to said user station, wherein;
Ii=rCAi+H(M)KeyCAi; and wherein
H(M) is an integer derived from said message M in accordance with a publicly known algorithm H, and rCAi is one of said random integers generated by, and KeyCAi is a private key of an ith one of said certifying authorities CA. A public key KeyCAi*P is published in any convenient manner for each of said certifying authorities CA; the user station is controlled to compute a private key KeyU, wherein
KeyU=rU+sum(Ii)=rU+sum(rCAi)+sum(H(M)KeyCAi.
A party wishing to communicate with the user then can compute said user""s public key KeyU*P as
KeyU*P=CERTU+H(M)*sum[+](KeyCAi*P)=(rU+sum(rCAi))*P+sum(H(M)KeyCAi)*P
from knowledge of H, M, [P], said public keys KeyCAi*P, and CERTU.
In accordance with an aspect of the subject invention the publicly known manner for deriving an integer from said published information comprises applying a hashing function to said message M.
In accordance with another aspect of the subject invention the message M includes information IDU identifying or characterizing said user U.
In accordance with another aspect of the subject invention the user station receives said random number rU from, and transmits said KeyU to an apparatus for evidencing payment, said apparatus generating encrypted indicia as proof of payment.
In accordance with another aspect of the subject invention one of said certifying stations is a registration station used by a registration authority said registration authority having responsibility for verifying said user""s identity and incorporating information IDu identifying or characterizing said user U.
In accordance with another aspect of the subject invention the apparatus comprises a postage meter for evidencing payment of postage.
In accordance with another aspect of the subject invention the registration authority is a supplier of said apparatus and another of said certifying stations is used by a postal service.
In accordance with another aspect of the subject invention the group [P] is defined on an elliptic curve.
In accordance with another aspect of the subject invention the message M includes information tying said user""s public key KeyU*P to said information IDU.
In accordance with still another aspect of the subject invention a public key of a user is certified by a plurality of certifying authorities, each of said certifying authorities having a published public key and a corresponding private key, by a method wherein said certifying authorities provide said user with integers, each of said integers being a first function of one of said private keys for a corresponding one of said authorities; said user computes a private key as a second function of said integers; and at least one of said certifying authorities publishes related information; wherein said first function, said second function and said published related information are chosen so that a party communicating with said user can compute said user public key, corresponding to said computed private key, by operating on said published related information with a summation of said published public keys of said authorities.
In accordance with still yet another aspect of the subject invention the user employs an apparatus for evidencing payment which generates said random number rU and transmits rU*P to said user. The user then transmits said integers Ii to said apparatus, said apparatus computing said private key by combining said integers Ii with rU, and generating encrypted indicia as proof of payment.
In accordance with still yet another aspect of the subject invention one of said certifying authorities is a registration authority, said registration authority having responsibility for verifying said user""s identity and incorporating said information identifying or characterizing said user.
In accordance with still yet another aspect of the subject invention the registration authority is a supplier of said apparatus and another of said certifying authorities is a postal service.